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Transverse anisotropy in the mixed-valent Mn2IIMn4IIIMn3IV single-molecule magnet

26 Feb 2008-Journal of Applied Physics (American Institute of Physics)-Vol. 103, Iss: 7

Abstract: High-frequency electron paramagnetic resonance measurements have been performed on a single-crystal sample of a recently discovered mixed valent Mn2IIMn4IIIMn3IV single-molecule magnet, with a spin S=17∕2 ground state. Frequency, temperature and field-orientation dependent studies confirm previously reported axial magnetic anisotropy parameters and also provide clear evidence for higher order (fourth and sixth) transverse terms that are responsible for the magnetic quantum tunneling observed in this system.

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Transverse anisotropy in the mixed-valent (Mn2Mn4Mn3IV)-Mn-II-
Mn-III single-molecule magnet
Citation for published version:
Datta, S, Milios, CJ, Brechin, E & Hill, S 2008, 'Transverse anisotropy in the mixed-valent (Mn2Mn4Mn3IV)-
Mn-II-Mn-III single-molecule magnet', Journal of applied physics, vol. 103, no. 7, 07B913, pp. -.
https://doi.org/10.1063/1.2838339
Digital Object Identifier (DOI):
10.1063/1.2838339
Link:
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Download date: 09. Aug. 2022

Transverse anisotropy in the mixed-valent Mn2IIMn4IIIMn3IV single-
molecule magnet
Saiti Datta, Constantinos J. Milios, Euan Brechin, and Stephen Hill
Citation: J. Appl. Phys. 103, 07B913 (2008); doi: 10.1063/1.2838339
View online: http://dx.doi.org/10.1063/1.2838339
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Transverse anisotropy in the mixed-valent Mn
2
II
Mn
4
III
Mn
3
IV
single-molecule
magnet
Saiti Datta,
1,a
Constantinos J. Milios,
2
Euan Brechin,
2
and Stephen Hill
1
1
Department of Physics, University of Florida, Gainesville, Florida 32611, USA
2
School of Chemistry, University of Edinburgh, West Mains Road, Edinburgh, EH9 3JJ, United Kingdom
Presented on 9 November 2007; received 12 September 2007; accepted 29 November 2007;
published online 26 February 2008
High-frequency electron paramagnetic resonance measurements have been performed on a
single-crystal sample of a recently discovered mixed valent Mn
2
II
Mn
4
III
Mn
3
IV
single-molecule magnet,
with a spin S=17/ 2 ground state. Frequency, temperature and field-orientation dependent studies
confirm previously reported axial magnetic anisotropy parameters and also provide clear evidence
for higher order fourth and sixth transverse terms that are responsible for the magnetic quantum
tunneling observed in this system. © 2008 American Institute of Physics.
DOI: 10.1063/1.2838339
INTRODUCTION
Mixed-valent manganese clusters are considered ideal
candidates for single-molecule magnets SMMs as they of-
ten a exhibit large spin ground states and b possess Jahn–
Teller distorted Mn
3
III
ions which contribute to a large easy-
axis-type magnetic anisotropy.
1
These nanosized magnetic
materials display magnetization hysteresis and quantum tun-
neling of magnetization
2,3
QTM suggesting that they may
one day find applications in information storage and possibly
quantum computation.
Here, we present single-crystal high-frequency electron
paramagnetic resonance HFEPR studies of a mixed valent
Mn
2
II
Mn
4
III
Mn
3
IV
complex hereafter Mn
9
Ref. 4兲兴, confirming
the main findings of previous magnetic measurements and
inelastic neutron scattering INS studies, which showed that
Mn
9
has a spin ground state of S =17/ 2, a dominant axial
anisotropy parameterized by a D of value −0.24 cm
−1
, to-
gether with a fourth-order axial zero-field splitting ZFS
term B
4
0
= +6.6810
−6
cm
−1
. Crucially, the present study
provides clear evidence for higher-order fourth and even
sixth order transverse anisotropy terms, which will clearly
influence the tunneling.
EXPERIMENTAL
The Mn
9
O
7
O
2
CCH
3
11
thme兲共py
3
H
2
O
2
complex
was prepared as reported previously.
4,5
Good sized black
crystals were obtained for single-crystal HFEPR measure-
ments. The metallic skeleton of the complex can be thought
to comprise two rings: a smaller Mn
3
IV
O
10+
triangle within a
Mn
4
III
Mn
2
II
O
6
4+
hexagon the charge is compensated by the
ligands. At first sight, the magnetic core appears to have a
pseudothreefold topology. However, closer inspection of the
Mn valence states on the outer hexagon reveal a much lower
symmetry.
5
All of the Mn ions are in distorted octahedral
geometries with the Jahn–Teller elongation of the Mn
3+
ions
lying almost perpendicular to the plane of the
Mn
4
III
Mn
2
II
O
6
4+
hexagon. The complex crystallizes such that
there are two symmetry-equivalent, but differently oriented
molecules in the unit cell whose magnetic easy axes are ap-
proximately perpendicular to each other.
HFEPR experiments were performed on a single crystal
at various temperatures and frequencies from 50 to 200 GHz
with the dc magnetic field applied along different crystallo-
graphic directions. The spectra were obtained at fixed fre-
quencies and temperatures while varying the strength of the
dc magnetic field. Details of the experimental technique can
be found elsewhere.
6,7
DATA AND DISCUSSION
Single-axis rotation studies were first performed to
roughly determine the orientation of the crystal in the mag-
netic field. Figure 1 shows temperature dependent spectra
obtained at 120 GHz, with the field oriented reasonably close
30° to the easy axis associated with one of the two sites in
the unit cell. The intensities of the lowest field peaks de-
crease upon increasing the temperature. This can be ex-
a
Electronic mail: saiti@ufl.edu.
FIG. 1. Color online Temperature dependent EPR spectra obtained at
120 GHz with the field oriented reasonably close 30° to the easy axis of
one of the two molecular orientations. Each set of fine structures is further
split into peaks labeled A and B, corresponding to inequivalent molecular
species with slightly different ZFS parameters D. See main text for expla-
nation of numbering.
JOURNAL OF APPLIED PHYSICS 103, 07B913 2008
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plained assuming a negative uniaxial anisotropy D 0. The
appearance of two sets of peaks in Fig. 1 indicates that, in
addition to the two different molecular orientations, there
exist inequivalent Mn
9
species with slightly different ZFS
parameters. We label the stronger peaks A and the weaker
ones B. Peaks 1, 2, 3, 4, and 5 correspond to the following
fine-structure transitions: m
S
=−
17
2
15
2
,−
15
2
13
2
,−
13
2
11
2
,−
11
2
9
2
, and
9
2
7
2
, respectively, where m
S
repre-
sents the spin projection along the easy z axis of the crys-
tal.
Figures 2a and 2b display the positions of the ob-
served EPR peaks plotted versus frequency for species A and
B, and for the same field orientation as the data displayed in
Fig. 1. The solid curves were simulated using the following
spin Hamiltonian Eq. 1, containing only axial ZFS pa-
rameters
H
ˆ
= DS
ˆ
z
2
+ B
4
0
35S
ˆ
z
4
30SS +1兲其S
ˆ
z
2
+
B
B · g
J
· S
ˆ
. 1
The simulations assume S=
17
2
, and best overall agreement
with the data is obtained with D=−0.24 cm
−1
D =
−0.25 cm
−1
for species A species B, B
4
0
= +6.68
10
−6
cm
−1
and g
z
=1.98. It is well documented that low-
field data especially extrapolations to B =0 obtained for
fields close to the easy axis are insensitive to transverse an-
isotropy terms.
8
As can be seen from Table I, the obtained
axial parameters agree very well with previous magnetic and
spectroscopic measurements.
4,5
Rotation about a single axis guarantees field-alignment
in the hard plane, although the orientation of the field within
the hard plane is not known. Detailed studies not shown
allow identification of one or other of the hard plane orien-
tations from the angle dependence of the peak positions see
Ref. 9. Figure 3a displays temperature dependent 52 GHz
spectra for one of these hard-plane orientations. The A and B
peaks are again observed, corresponding to the two species.
The reversed ordering of A and B see Fig. 1 is consistent
with Eq. 1. Peaks labeled A 1
,A3
, and A5
likewise for
the B peaks correspond to the following fine-structure tran-
sitions: m
S
=−
17
2
15
2
,−
13
2
11
2
, and
9
2
7
2
, respectively,
where m
S
now represents the spin projection along the high
magnetic field quantization axis. The low field portion of the
figure fields below A5
is complicated by absorptions due
to the other molecular orientation.
We now argue that fourth and higher-order transverse
ZFS interactions are necessary in order to account for these
spectra. It is well documented that HFEPR measurements
FIG. 2. Frequency dependence of the peak positions associated with the
two species: a Aandb B. Data were obtained at 5 K for the same field
orientation as in Fig. 1. The solid lines are simulations based on Eq. 1,
using the parameters given in the main text.
TABLE I. Comparison between ZFS parameters obtained from these studies EPR and the various magnetic
measurements reported in Refs. 4 and 5.
ZFS
cm
−1
FDMRS INS Magnetization
-SQUID DFT
EPR
A
EPR
B
D −0.2475 −0.2495 −0.293 −0.258 −0.235 −0.24 −0.25
B
4
0
/ 10
−6
4.61 74 6.7 6.7
FIG. 3. Color online兲共a Temperature dependent EPR spectra obtained at
52 GHz with the field in the hard plane of one of the molecular orientations.
The fine structure splitting A and B peaks can again be clearly seen refer
to main text for explanation of numbering. At the highest temperature,
additional peaks appear labeled X which we attribute to excited spin mul-
tiplets. b Frequency dependence of the 7 K hard plane peak positions
associated with species A the dashed curve corresponds to the data in a兲兴.
The orientation of the field within the hard plane is not known. The curves
correspond to various simulations based on Eq. 1 with the inclusion of a
rhombic term ES
ˆ
x
2
S
ˆ
y
2
兲兴. See main text for explanation.
07B913-2 Datta et al. J. Appl. Phys. 103, 07B913 2008
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with B c provide information concerning transverse terms.
8
In the following analysis, we constrain the axial terms D
and B
4
0
on the basis of the simulations in Fig. 2. Density
functional theory DFT calculations predict that Mn
9
pos-
sesses a rhombohedral ZFS parameter E = 0.035 cm
−1
.
5
We
find that it is impossible to obtain agreement between our
results and simulations including only this interaction ES
ˆ
x
2
S
ˆ
y
2
兲兴, as demonstrated in Fig. 3b. The black curves were
generated for two different E values and field orientations
relative to the hard axis within the hard plane: E
=0.035 cm
−1
,
=25°; and E=0.015 cm
−1
,
=0° i.e., B
x.
These parameters were chosen in order to obtain agreement
between the simulations and the A1
peak. However, as can
be seen, agreement with A3
is not good. Conversely, the red
curves were generated with the following parameters: E
=0.035 cm
−1
,
=40° and E = 0.015 cm
−1
,
=38° i.e., B
x.
Here, the goal was to achieve agreement with the A3
peak.
g
x
and g
y
were set to 2.00 for all of these simulations, as well
as those in Fig. 4. The main result is that it is impossible to
obtain anything approaching agreement with more than one
of these peaks using only an E parameter.
It turns out that, with the exception of A1
, all EPR
peaks are reasonably close to the positions one would expect
for extremely weak transverse second order anisotropy or
=45°. In contrast, A1
is shifted considerably to higher
fields. It is only possible to mimic its behavior using higher
order transverse terms, as illustrated in Fig. 4. In fact, one
can obtain good agreement with the hard-plane spectra for
several different parameter sets. Examples are displayed in
Fig. 4 involving purely B
4
2
O
ˆ
4
2
a and B
6
6
O
ˆ
6
6
b. The coeffi-
cients are given in the captions. Interestingly, B
6
6
O
ˆ
6
6
gives
excellent agreement, whereas terms that one might expect to
work well, such as B
4
3
O
ˆ
4
3
, do not give good agreement. In
reality, it is likely that the transverse Hamiltonian involves
admixtures of all of these interactions, reflecting the
pseudothreefold,
5
albeit low symmetry of the molecule. Only
detailed multihigh-frequency measurements performed as a
function of the field orientation within the hard plane can
resolve this issue, which would be greatly complicated by
the multiple species, orientations, and the overall low sym-
metry of this complex. Nevertheless, the present measure-
ments serve a useful purpose, hinting at the significant fourth
and higher-order anisotropy that likely results as a conse-
quence of S mixing brought about by low-lying excited spin
states.
10
Indeed, the spectra in Fig. 3a clearly show features
labeled X associated with the population of low-lying S
17
2
spin states.
One final point to note from Fig. 4a is the huge tunnel
splitting of the lowest-lying m
S
=
17
2
doublet, which is
clearly visible to the naked eye down to low fields. This
suggests that a B
4
2
O
ˆ
4
2
interaction would cause very fast tun-
neling in this Mn
9
complex, which is not found experimen-
tally and, therefore, seems to be unphysical. Again, this hints
at the importance of multiple high-order transverse ZFS in-
teractions that can account for both the EPR data presented
here and the slow magnetization dynamics in the quantum
regime. We also note that internal dipolar and hyperfine
fields must be important for zero-field QTM in these half
integer SMMs.
CONCLUSIONS
Multi-high frequency and field orientation dependent
EPR studies have enabled a detailed characterization of the
spin Hamiltonian of a mixed valent Mn
9
complex. These
measurements hint at the importance of high- fourth and
sixth order transverse anisotropy terms in the low tempera-
ture quantum dynamics.
ACKNOWLEDGMENTS
This work was supported by the NSF DMR0239481
and DMR0506946.
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FIG. 4. Color online Hard-plane data from Fig. 3 and simulations based
on Eq. 1, with the additional inclusion of the higher-order transverse in-
teractions a B
4
2
O
ˆ
4
2
and b B
6
6
O
ˆ
6
6
actual functions given in the figures. Both
simulations agree reasonably well with the experimental data using the axial
ZFS parameters determined from the simulations in Fig. 2, along with the
following parameters: a B
4
2
=8.4 10
−5
cm
−1
, b B
6
6
=8.4 10
−7
cm
−1
, and
=0 for both a and b. See main text for detailed explanation. The blue
curves correspond to the splitting in the ground state m
S
=
17
2
doublet.
07B913-3 Datta et al. J. Appl. Phys. 103, 07B913 2008
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Figures (5)
Citations
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TL;DR: It is proposed that these effects are manifestations of thermally assisted, field-tuned resonant tunneling between quantum spin states, and attribute the observation of quantum-mechanical phenomena on a macroscopic scale to tunneling in a large (Avogadro's) number of magnetically identical molecules.
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Abstract: We describe instrumentation for conducting high sensitivity millimeter-wave cavity perturbation measurements over a broad frequency range (40–200 GHz) and in the presence of strong magnetic fields (up to 33 T). A millimeter-wave vector network analyzer (MVNA) acts as a continuously tunable microwave source and phase sensitive detector (8–350 GHz), enabling simultaneous measurements of the complex cavity parameters (resonance frequency and Q value) at a rapid repetition rate (∼10 kHz). We discuss the principle of operation of the MVNA and the construction of a probe for coupling the MVNA to various cylindrical resonator configurations which can easily be inserted into a high field magnet cryostat. We also present several experimental results which demonstrate the potential of the instrument for studies of low-dimensional conducting systems.

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E. del Barco1, E. del Barco2, Andrew D. Kent2, Stephen Hill3  +6 moreInstitutions (5)
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